Rhinitis is not exactly a disease. It's just a matter of your body getting used to it. Most likely it disturbs existing dust. Also - does your house have proper ventilation system? In high co2 environments I get rhinitis too.
Did you ask them? Not even billions, did you ask at least a few thousand? Nobody complained? I know for a fact many people working in buildings with forced AC complain loudly.
But if you actually did read what I wrote, there was no complaint from me about the cooling part of the AC.